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arXiv · 2603.22896

V-shaped transition fronts of monotone bistable reaction-diffusion systems in exterior domains

Yang-Yang Yan·Wei-Jie Sheng
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Abstract

This paper investigates the propagation phenomena of a monotone bistable reaction-diffusion system in an exterior domain of R2. By constructing suitable sub- and supersolutions, we establish the existence and monotonicity of an entire solution originating from a V-shaped traveling front. It is further shown that, under the complete propagation condition, this entire solution eventually recovers its V-shaped profile as time tends to infty after passing the obstacle. In particular, we show that the entire solution is a V-shaped transition front whose global mean speed coincides with the planar wave speed.

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Yang-Yang Yan, Wei-Jie Sheng. 2026-03-24. V-shaped transition fronts of monotone bistable reaction-diffusion systems in exterior domains. https://arxiv.org/abs/2603.22896

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